Ink removal is one of the most important steps in recycling of mixed office wastepaper, old magazine, and old newsprint. Ink removal efficiency of a recycling operation is characterized by the brightness increment of the final paper over that of feed stock. Final paper brightness has been used as a product specification of recycled papers. However, the brightness measure has deficiencies in quantifying ink-removal efficiency and the amount of residual ink in de-inked pulp because paper brightness depends on additional factors, such as pulp refining, pressing, calendering, and formation. Jordan and Popson developed a radiation reflectance technique to measure residual ink concentration in paper made of de-inked pulp using Kubelka-Munk theory. The technique measures reflectance at an infrared wavelength (˜950 nm) from a paper sample over a black backing, R0, and reflectance from a thick stack of paper from the same sample, R∞. The Kubelka-Munk constant k, the specific absorption coefficient of the sample, can be calculated from the two measured reflectance values, R0 and R ∞. It is directly related to the residual ink concentration in the paper sample when measured at a near infrared wavelength where the absorption from lignin and dyes can be ignored.
According to this approach, the specific absorption coefficient, k, is
  k  =      s    ⁢                            (                      1            -                          R              ∞                                )                2                    2        ⁢                                  ⁢                  R          ∞                    where the specific scatter coefficient, s, is
  s  =            [                        R          ∞                          w          ⁡                      (                          1              -                              R                ∞                2                                      )                              ]        ⁢          ln      ⁡              [                              1            -                                          R                0                            ⁢                              R                ∞                                                          1            -                                          R                0                            ⁢                              /                            ⁢                              R                ∞                                                    ]            and w is the basis weight.
In particular, the commonly used approach employs a detector measuring the reflected radiation from a test paper. The paper specimen is removed, placed in front of a stack of equivalent papers, and replaced with the stack in the sample holder. At this time, the reflected radiation is measured a second time. The two values of reflected radiation are used to determine ERIC. Problems with this method occur when the samples are so opaque to the radiation that both values are the same, or nearly so. In that case the equation to calculate ERIC leads to inaccurate values. The remount of the test specimen on the stack also induces error in measurement because the specimen cannot be repositioned exactly as it was. The degree of contact between the papers in the stack also changes, introducing further measurement variability.
This accepted method for measuring effective residual ink concentration (ERIC) in recycled papers is limited to papers having opacity values less than 97.0. This is because the method is based on diffuse reflection from papers measured once with a black backing and again with a thick backing of similar papers. The two reflection values become statistically indistinguishable at high opacities. ERIC values are undetermined owing to a logarithmic singularity in the defining equation. Even when ERIC values can be calculated, their uncertainty is amplified by the singularity to the point where predicted coefficients of variation (COV) exceed 50% in papers near the opacity limit. For example, in five repeat tests of a sample containing five similar handsheets, individual ERIC values ranged from 309 to 858 ppm, even though the average opacity for the sample was an acceptable 96.1. The lower end of this range is close to the average ERIC for commercial papers, whereas the upper end is close to three times the commercial average. This renders the test marginally useful as a way to monitor the de-inking process.